7 1/2 ÷ 3 3/4 equals?

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.11 millimeters and a standard deviat

____ [38]

Answer:

The diameter that separates the bottom 9% is 5.02 millimeters.

The diameter that separates the top 9% is 5.2 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.11 millimeters and a standard deviation of 0.07 millimeters.

This means that $\mu = 5.11, \sigma = 0.07$

Bottom 9%:

The 9th percentile, which is X when Z has a pvalue of 0.09. So X when Z = -1.34.

$Z = \frac{X - \mu}{\sigma}$

$-1.34 = \frac{X - 5.11}{0.07}$

$X - 5.11 = -1.34*0.07$

$X = 5.02$

The diameter that separates the bottom 9% is 5.02 millimeters.

Top 9%:

The 100 - 9 = 91th percentile, which is X when Z has a pvalue of 0.91. So X when Z = 1.34.

$Z = \frac{X - \mu}{\sigma}$

$1.34 = \frac{X - 5.11}{0.07}$

$X - 5.11 = 1.34*0.07$

$X = 5.2$

The diameter that separates the top 9% is 5.2 millimeters.

6 0

2 years ago

Renaldo catches the bus at 4:00 pm to ride 3.2 miles from his house to the dentists office. he arrives at 4:30 pm, for a one hou

andrew11 [14]

Answer:

Step-by-step explanation:

speed = distance/time

so renaldo speed = 3.2/0.5 = 6.4miles/hr (since time taken is 1/2 hr)

now after 1 hr of his appoinment i.e at 5:30pm he took bus whose speed is same as before i.e 6.4 miles/hr

now time taken to cover this 4.8 miles = 4.8/6.4 = 3/4 hr (since time = distance /speed )

3/4 hr = 3/4 * 60 = 45 minutes

so he reached at 6:15pm . so he will be on time.

8 0

2 years ago

What is the approximate value for the modal daily sales?

Aleksandr [31]

Answer:

Step-by-step explanation:

Hello!

The table shows the daily sales (in $1000) of shopping mall for some randomly selected days 

Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5 

Days 18 27 31 40 56 55 23 

Use it to answer questions 13 and 14. 

13. What is the approximate value for the modal daily sales? 

To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)

The modal interval is [3.1-3.5]

Now using the following formula you can calculate the Mode:

$Md= Li + c[\frac{(f_{max}-f_{prev})}{(f_{max}-f_{prev})(f_{max}-f_{post})} ]$

Li= Lower limit of the modal interval.

c= amplitude of modal interval.

fmax: absolute frequency of modal interval.

fprev: absolute frequency of the previous interval to the modal interval.

fpost: absolute frequency of the posterior interval to the modal interval.

$Md= 3,100 + 400[\frac{(56-40)}{(56-40)+(56-55)} ]= 3,476.47$

A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53 

Of all options the closest one to the estimated mode is A.

14. The approximate median daily sales is … 

To calculate the median you have to identify its position first:

For even samples: PosMe= n/2= 250/2= 125

Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.

F(1)= 18

F(2)= 18+27= 45

F(3)= 45 + 31= 76

F(4)= 76 + 40= 116

F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]

$Me= Li + c[\frac{PosMe-F_{i-1}}{f_i} ]$

Li: Lower limit of the median interval.

c: Amplitude of the interval

PosMe: position of the median

F(i-1)= accumulated absolute frequency until the previous interval

fi= simple absolute frequency of the median interval.

$Me= 3,100+400[\frac{125-116}{56} ]= 3164.29$

A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664

Of all options the closest one to the estimated mode is C.

5 0

2 years ago

254 cm to inches with explanation please

sdas [7]

Answer:

100 inch

Step-by-step explanation:

1 cm=0.394 inch

254 cm×0.394=100 inch

4 0

2 years ago

Read 2 more answers

CAN ANYONE HELP ME ON THIS

SpyIntel [72]

Answer:

i can help

Step-by-step explanation:

what the question

7 0

2 years ago